Since melanocytes respond to light and babies are in the comfort and darkness of the womb, they have little melanin, and therefore mostly blue eyes when they're born.
When my daughter turned two-and-a-half, I realised that her eyes were starting to shift away from the baby blues she was born ...
Go ahead and enjoy gazing into those baby blues (or greens, or browns …), but keep in mind that your newborn's eye color may not be permanent! There are no hard and fast rules, but a baby's eye ...